Helfrich¶

class hoomd.md.mesh.bending.Helfrich(mesh)¶

Bases: MeshPotential

Helfrich bending potential.

Parameters:: mesh (hoomd.mesh.Mesh) – Mesh data structure constraint.

Helfrich specifies a Helfrich bending energy applied to all particles within the mesh.

U(i) = \frac{1}{2} k \frac{1}{\sigma_i}\left( \sum_{j \in \mathrm{Neigh}(i)} \frac{\sigma_{ij}}{l_{ij}} (\mathbf{r}_j - \mathbf{r}_k) \right)^2

with the area of the dual cell of vertex i $\sigma_i=(\sum_{j \in \mathrm{Neigh}(i)}\sigma_{ij})/4$ , the length of the bond in the dual lattice $\sigma_{ij}= r_{ij}(\text{cot}\theta_1+\text{cot}\theta_2)/2$ and the angles $\theta_1$ and $\theta_2$ opposite to the shared bond of vertex $i$ and $j$ .

See also

Attention

Helfrich is NOT implemented for MPI parallel execution!

Example:

helfrich_potential = hoomd.md.mesh.bending.Helfrich(mesh)
helfrich_potential.params["mesh"] = dict(k=10.0)

Members inherited from AutotunedObject:

property kernel_parameters¶: Kernel parameters. Read more...

property is_tuning_complete¶: Check if kernel parameter tuning is complete. Read more...

tune_kernel_parameters()¶: Start tuning kernel parameters. Read more...

Members inherited from Force:

additional_energy¶: Additional energy term. Read more...

additional_virial¶: Additional virial tensor term $W_\mathrm{additional}$ . Read more...

cpu_local_force_arrays¶: Local force arrays on the CPU. Read more...

energies¶: Energy contribution $U_i$ from each particle. Read more...

energy¶: The potential energy $U$ of the system from this force. Read more...

forces¶: The force $\vec{F}_i$ applied to each particle. Read more...

gpu_local_force_arrays¶: Local force arrays on the GPU. Read more...

torques¶: The torque $\vec{\tau}_i$ applied to each particle. Read more...

virials¶: Virial tensor contribution $W_i$ from each particle. Read more...

Members inherited from MeshPotential:

mesh¶: Mesh data structure used to compute the bond potential. Read more...

Members defined in Helfrich:

params¶

The parameter of the Helfrich energy for the defined mesh. As the mesh can only have one type a type name does not have to be stated. The dictionary has the following keys:

k (float, required) - bending stiffness $[\mathrm{energy}]$

Type:: TypeParameter[dict]